Nonuniform dichotomic behavior: Lipschitz invariant manifolds for difference equations

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results are obtained using Banach fixed point theorem and include situations where the behavior is far from hyperbolic. We also give several new examples and show that our result includes as particular cases several previous theorems.